We extend the basic random walk Markov-Switching model in two ways and evaluate the out-of-sample forecasting performance on the Japanese yen during 1995-2004. First, we estimate both a twoand also a three-regime Markov switching models. Second, we add four exogenous variables as suggested in the monetary theory. According to the modified DieboldMariano forecast equivalence test, the result sho...

What happens when a quantum system undergoing unitary evolution in time is subject to repeated projective measurements the initial state at random times? A question of general interest is: How does survival probability $S_m$, namely, that an survives even after $m$ number measurements, behave as function $m$? We address these issues context two paradigmatic systems, one, walk evolving discrete ...

In this paper we present a random walk model for approximating a Lévy-Feller advection-dispersion process, governed by the Lévy-Feller advection-dispersion differential equation (LFADE). We show that the random walk model converges to LFADE by use of a properly scaled transition to vanishing space and time steps. We propose an explicit finite difference approximation (EFDA) for LFADE, resulting...

We present and compare two delayed random walk models of neural information processing. A delayed random walk is a random walk in which the transition probability depends on the position of the walker at a time in the past. The rst model is of human neuro-muscular control for postural sway. The other model is for a stochastic single neuron which has a delayed self{exciting feedback. We study ea...

Multi-document summarization provides users with a short text that summarizes the information in a set of related documents. This paper introduces affinitypreserving random walk to the summarization task, which preserves the affinity relations of sentences by an absorbing random walk model. Meanwhile, we put forward adjustable affinity-preserving random walk to enforce the diversity constraint ...